1. Field of the Invention
This invention relates to the field of seismic data processing. More particularly, this invention relates to a method of obtaining improved spatial and/or temporal resolution of 2-D or 3-D seismic data.
2. Background of the Art
A seismic survey represents an attempt to map the subsurface of the earth by sending acoustic or elastic energy down into the ground and recording the xe2x80x9cechoesxe2x80x9d that return from the rock layers below. The source of the downgoing acoustic or elastic energy might come, for example, from explosions or seismic vibrators on land, and air guns in marine environments. During a seismic survey, the energy source is moved across the surface of the earth above a geologic structure of interest. Each time the source is actuated, it generates a seismic signal that travels downward through the earth, is reflected and/or diffracted, and, upon its return, is recorded at a great many locations on the surface. Multiple source-actuation/recording combinations are then combined to create a near continuous profile of the subsurface that can extend for many kilometers. In a two-dimensional (2-D) seismic survey, the source and recording locations are generally laid out along a single straight line, whereas in a three-dimensional (3-D) survey the source and recording locations are generally distributed across the surface in a grid pattern. In simplest terms, a 2- D seismic line can be thought of as giving a cross sectional picture (vertical slice) of the earth layers with reflector locations roughly midway between the source positions and the receiver positions. A 3-D survey produces a data xe2x80x9ccubexe2x80x9d or volume that is, at least conceptually, a 3-D picture of the subsurface that lies beneath the survey area with reflector positions roughly midway between the source positions and the receiver positions in the acquisition grid.
A seismic survey is composed of a very large number of individual seismic recordings or traces. In a typical 2-D survey, there will usually be several tens of thousands of traces, whereas in a 3-D survey the number of individual traces may run into the multiple millions of traces. General background information pertaining to 3-D data acquisition and processing may be found in Chapter 6, pages 384-427, of Seismic Data Processing by Ozdogan Yilmaz, Society of Exploration Geophysicists, 1987, the disclosure of which is incorporated herein by reference.
Unprocessed seismic data is only of limited use to an explorationist. Seismic data as it is acquired in the field is seldom used directly, but instead it is first returned to a processing center where various mathematical algorithms are applied to the digital seismic data to enhance its signal content and generally make it more amenable to interpretation. A key step in a typical seismic processing sequence is seismic migration.
As is well known to those skilled in the art, the dip, location and character of a reflector on an unmigrated seismic section is rarely representative of the true dip, subsurface location and character of the structural or stratigraphic feature that gave rise to that reflector. Except in the case where the subsurface consists of homogenous, horizontal layers, the recorded seismic expression of a structural or stratigraphic event must be migrated before it can be reliably used to locate subsurface features of interest. In areas of steep dip, a reflection that is apparently located directly below a particular surface point before migration may, after migration, actually be found several hundreds of meters away. Additionally, in complex structural areas where faulting, severe asymmetrical folding and sharp synclines are present, diffractions and multiple reflections may interfere with reflections from the primary reflectors to the point where, without migration, the resulting seismic section bears little or no resemblance to the actual subsurface structure.
Broadly speaking, migration improves a seismic section or volume by xe2x80x9cfocusingxe2x80x9d the seismic data contained therein, a process that is conceptually similar to that of xe2x80x9cfocusingxe2x80x9d the image produced by a slide projector in order to obtain the sharpest screen image. Migration improves the seismic image by correcting the lateral mispositioning of dipping seismic reflectors; collapsing diffractions caused by point scattering centers and subsurface fault terminations; resolving crossing reflectors (conflicting dips); and improving the vertical and lateral resolution of the seismic data, among many others. A general description of the many ways that migration improves seismic data may be found in, for example, Chapters 4 and 5, and Appendix C, pages 240-383, and 507-518, of Seismic Data Processing by Ozdogan Yilmaz, Society of Exploration Geophysicists, 1987, the disclosure of which is incorporated herein by reference. As a general rule, seismic data that have been properly migrated reveal an enhanced or a truer picture of the subsurface than unmigrated seismic data, the ultimate goal of seismic migration being to produce a seismic section or volume that accurately represents the configuration and character of the geology of the subsurface.
U.S. Pat. No. 6,049,759 to Etgen discloses a method of prestack migration of 3-D seismic data. As taught therein, there are two broad variants of seismic migration: migration after stack (poststack) and migration before stack (prestack). Post- stack migration is applied, as the name suggests, to seismic traces after they have been stackedxe2x80x94a stacked seismic trace being one that is formed by combining together two or more traces after Normal-Moveout (NMO) correction to form a single composite trace that is an approximation of a zero offset trace at that location. Prestack migration, on the other hand, is applied to seismic traces before they have been stacked. Other things being equal prestack migration is always preferredxe2x80x94both theoretically and in practicexe2x80x94because it has the potential to produce a more accurate picture of the subsurface stratigraphy and structure. However, the computational effort involved in computing a prestack migration is many times that required to do a poststack migration. For 2-D seismic lines, this additional computational effort is generally manageable and, except for the longest lines, prestack migration is often applied to seismic data that has been taken in areas where the subsurface structure is complicated. Many 3-D data sets, on the other hand, contain far too many traces to be cost-effectively migrated via conventional prestack algorithms.
An attractive algorithm to approximate full prestack migration in 3-D and even for 2-D seismic acquisition is the use of Pre-stack Partial Migration, also known as Dip Moveout Correction (DMO). DMO moderates the effect of reflection-point smear and enables events to be stacked coherently moderating the effects of dip and/or azimuth. Thereafter the data can be stacked and post-stack migrated conventionally but with a substantial degree of data compression. An additional advantage is that DMO is a relatively small correction that tends to be insensitive to errors in the estimated velocity used for NMO corrections. This is a significant improvement over NMO-stack.
There are various alternative equivalent implementations of DMO. Perhaps the most popular are Hale""s method and the summation method of Deregowski and Rocca. Hale""s Fourier-based method, proposed in his doctoral thesis xe2x80x9cDip Moveout by Fourier Transformxe2x80x9d submitted to Stanford University Geophysics Department, May 1983, is carried out in frequency/wave vector (f,k) domain. Deregowski and Rocca""s summation method described in xe2x80x9cGeometrical Optics and Wave Theory of Constant Offset Sections in Layered Media,xe2x80x9d Geophysical Prospecting 29, 374-406 (1981), is carried out in time/space (t,x) domain. It involves summation of data along a xe2x80x9cDMO trajectory.xe2x80x9d
The migration and DMO methods disclosed in prior art and mentioned above start with digitally sampled data from a single seismic line or 2-D grid of seismic lines and obtain an output at locations that correspond to nominal positions of locations midway between the seismic sources and detectors used in the acquisition process. All of the time domain migration and DMO methods involve summation of data moved from an recorded position to an output position. In principle this is similar to what is performed in NMO correction of the data in a line of seismic data.
U.S. Pat. No. 5,596,546 to Wisecup teaches a method of preserving temporal frequency components in NMO corrected stack data that are normally lost in conventional NMO processing. Wisecup teaches the NMO correction of digital samples of offset seismic data to zero offset, where the NMO-corrected data may not fall at sampling time, and combining all such NMO-corrected contributions prior to resampling. This is in contrast to conventional NMO methods wherein an interpolation is done on the offset trace prior to NMO correction to ensure that the NMO-corrected samples fall on a discrete sampling time. The so-called Random Sample Interval Imaging (RSI2) method of Wisecup preserves more high frequency data than conventional NMO-stack methods. Analogous to and in addition to the loss of temporal frequencies in conventional processing, there is also a loss of spatial frequencies in conventional migration and DMO operations. The present invention is a method of preserving these higher temporal and spatial frequencies in partial or full migration of seismic data using the concepts taught by Wisecup.
In one aspect, the present invention is a method for preserving temporal frequencies in full or partial migration of a line of seismic data using, for example, DMO. This differs from the method of Wisecup in that instead of an NMO operation, data are migrated to discrete sampling locations defined by the source and/or receiver positions. These locations are commonly midway between sources and receivers. The migration may be a partial migration such as a DMO, or it may be any full time-or depth-domain migration such as a Kirchoff migration.
In another aspect of the invention, the present invention is a method of preserving temporal and spatial frequencies in full or partial migration of a line of seismic data. This is similar to the preservation of temporal frequencies mentioned above, but additionally, the output spatial locations may be in a location not limited to being midway between a source and receiver location. In yet another aspect of the invention, only higher spatial frequencies are preserved.
Finally, in yet another aspect of the invention, temporal and/or spatial frequencies are preserved during a full or partial 3-D migration of seismic data acquired using a 2-D surface grid or a plurality of 2-D seismic lines wherein the output grid for the migration may be different from the input grid.